{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:6CTC7YQ35DCVIVAGPUUBBEED6E","short_pith_number":"pith:6CTC7YQ3","canonical_record":{"source":{"id":"2606.02647","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-31T16:59:19Z","cross_cats_sorted":[],"title_canon_sha256":"536dacf2ce1086094a2979684ab663c2f03a1ccd0ca978ef0a846084a2f5b5df","abstract_canon_sha256":"2739c2ac243e0f6fc2d481f379f2d4cdd4cbebeb20b4d926406893df44b2c47f"},"schema_version":"1.0"},"canonical_sha256":"f0a62fe21be8c55454067d28109083f10483c94c845bb9fc868f482a2d72a0bb","source":{"kind":"arxiv","id":"2606.02647","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.02647","created_at":"2026-06-03T00:05:05Z"},{"alias_kind":"arxiv_version","alias_value":"2606.02647v1","created_at":"2026-06-03T00:05:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02647","created_at":"2026-06-03T00:05:05Z"},{"alias_kind":"pith_short_12","alias_value":"6CTC7YQ35DCV","created_at":"2026-06-03T00:05:05Z"},{"alias_kind":"pith_short_16","alias_value":"6CTC7YQ35DCVIVAG","created_at":"2026-06-03T00:05:05Z"},{"alias_kind":"pith_short_8","alias_value":"6CTC7YQ3","created_at":"2026-06-03T00:05:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:6CTC7YQ35DCVIVAGPUUBBEED6E","target":"record","payload":{"canonical_record":{"source":{"id":"2606.02647","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-31T16:59:19Z","cross_cats_sorted":[],"title_canon_sha256":"536dacf2ce1086094a2979684ab663c2f03a1ccd0ca978ef0a846084a2f5b5df","abstract_canon_sha256":"2739c2ac243e0f6fc2d481f379f2d4cdd4cbebeb20b4d926406893df44b2c47f"},"schema_version":"1.0"},"canonical_sha256":"f0a62fe21be8c55454067d28109083f10483c94c845bb9fc868f482a2d72a0bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T00:05:05.562463Z","signature_b64":"GTGCftjYmWMClI0BeSkpVmWlB9Bh4EXxx6+A4SAKAd3ofyaPL7GuaGAZGptD0lxD6JUJj4ItCxl7V5e5DakwAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0a62fe21be8c55454067d28109083f10483c94c845bb9fc868f482a2d72a0bb","last_reissued_at":"2026-06-03T00:05:05.562063Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T00:05:05.562063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.02647","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-03T00:05:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xHTdj6kpRevJKEFyMXPxj+D+5N/o/tezG04/xgZl1JH3xhT6b+oWUgtGKw1nJEYP0KOF/wxfMvxa4Ou486PbCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T07:38:01.490339Z"},"content_sha256":"4a08e106cc3181119ce4454108c6a7dc4d071e31200b36003e0422ca6119452d","schema_version":"1.0","event_id":"sha256:4a08e106cc3181119ce4454108c6a7dc4d071e31200b36003e0422ca6119452d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:6CTC7YQ35DCVIVAGPUUBBEED6E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the upper area bound for minimal graphs in the unit ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Qing Cui","submitted_at":"2026-05-31T16:59:19Z","abstract_excerpt":"A classical result establishes that the area of a minimal graph intersected with the unit ball is at most $2\\pi$. A natural question is whether this upper bound is sharp. In this note, we resolve this by constructing a sequence of minimal graphs via solutions to a Dirichlet problem. We show that the areas of these graphs tend to $2\\pi$, demonstrating that the bound is sharp."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02647","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.02647/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-03T00:05:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EnIxBJlgChB+jJGhnDM7NG8kjiYygCGIQoP7bZm/moVIm6HdRDUrr1JRXCYdLMBdobGnCNU3ygTAoqoae6xiCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T07:38:01.490859Z"},"content_sha256":"118d6f6a3392e4d4df7de21ee82a5d5eb29e9cf8dadb7da22837906ff3716be9","schema_version":"1.0","event_id":"sha256:118d6f6a3392e4d4df7de21ee82a5d5eb29e9cf8dadb7da22837906ff3716be9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6CTC7YQ35DCVIVAGPUUBBEED6E/bundle.json","state_url":"https://pith.science/pith/6CTC7YQ35DCVIVAGPUUBBEED6E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6CTC7YQ35DCVIVAGPUUBBEED6E/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-07T07:38:01Z","links":{"resolver":"https://pith.science/pith/6CTC7YQ35DCVIVAGPUUBBEED6E","bundle":"https://pith.science/pith/6CTC7YQ35DCVIVAGPUUBBEED6E/bundle.json","state":"https://pith.science/pith/6CTC7YQ35DCVIVAGPUUBBEED6E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6CTC7YQ35DCVIVAGPUUBBEED6E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:6CTC7YQ35DCVIVAGPUUBBEED6E","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2739c2ac243e0f6fc2d481f379f2d4cdd4cbebeb20b4d926406893df44b2c47f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-31T16:59:19Z","title_canon_sha256":"536dacf2ce1086094a2979684ab663c2f03a1ccd0ca978ef0a846084a2f5b5df"},"schema_version":"1.0","source":{"id":"2606.02647","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.02647","created_at":"2026-06-03T00:05:05Z"},{"alias_kind":"arxiv_version","alias_value":"2606.02647v1","created_at":"2026-06-03T00:05:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02647","created_at":"2026-06-03T00:05:05Z"},{"alias_kind":"pith_short_12","alias_value":"6CTC7YQ35DCV","created_at":"2026-06-03T00:05:05Z"},{"alias_kind":"pith_short_16","alias_value":"6CTC7YQ35DCVIVAG","created_at":"2026-06-03T00:05:05Z"},{"alias_kind":"pith_short_8","alias_value":"6CTC7YQ3","created_at":"2026-06-03T00:05:05Z"}],"graph_snapshots":[{"event_id":"sha256:118d6f6a3392e4d4df7de21ee82a5d5eb29e9cf8dadb7da22837906ff3716be9","target":"graph","created_at":"2026-06-03T00:05:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.02647/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A classical result establishes that the area of a minimal graph intersected with the unit ball is at most $2\\pi$. A natural question is whether this upper bound is sharp. In this note, we resolve this by constructing a sequence of minimal graphs via solutions to a Dirichlet problem. We show that the areas of these graphs tend to $2\\pi$, demonstrating that the bound is sharp.","authors_text":"Qing Cui","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-31T16:59:19Z","title":"On the upper area bound for minimal graphs in the unit ball"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02647","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4a08e106cc3181119ce4454108c6a7dc4d071e31200b36003e0422ca6119452d","target":"record","created_at":"2026-06-03T00:05:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2739c2ac243e0f6fc2d481f379f2d4cdd4cbebeb20b4d926406893df44b2c47f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-31T16:59:19Z","title_canon_sha256":"536dacf2ce1086094a2979684ab663c2f03a1ccd0ca978ef0a846084a2f5b5df"},"schema_version":"1.0","source":{"id":"2606.02647","kind":"arxiv","version":1}},"canonical_sha256":"f0a62fe21be8c55454067d28109083f10483c94c845bb9fc868f482a2d72a0bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0a62fe21be8c55454067d28109083f10483c94c845bb9fc868f482a2d72a0bb","first_computed_at":"2026-06-03T00:05:05.562063Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T00:05:05.562063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GTGCftjYmWMClI0BeSkpVmWlB9Bh4EXxx6+A4SAKAd3ofyaPL7GuaGAZGptD0lxD6JUJj4ItCxl7V5e5DakwAg==","signature_status":"signed_v1","signed_at":"2026-06-03T00:05:05.562463Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.02647","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a08e106cc3181119ce4454108c6a7dc4d071e31200b36003e0422ca6119452d","sha256:118d6f6a3392e4d4df7de21ee82a5d5eb29e9cf8dadb7da22837906ff3716be9"],"state_sha256":"33bf45f7277b34f873b4c115ffc53beb2e93caf59f80105aba42b7920c24f887"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TQFiOMtnmlrNMszxYsUYxb0fvINd9/2HBtoXcjMjHXrgyzB/7TLQ/ryWasBYFCzXJFADX9CMm4aqR1rX+SSdBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T07:38:01.494313Z","bundle_sha256":"2e2b44b52c960b9497e9a76404ebe2fd6203e91e79d8eed52077252b809a712f"}}